Full confession as I haven't played any of the original XCOM games. So I don't have much in my mind in terms of if the game follows the originals legacy or anything. If you played the original and then this recent version shout out in the comments or another post, I am interested how that turned out for you.
XCOM is a turn based squad game. Basically its similar to something like Final Fantasy Tactics or the like where you take turns against the computer to overwhelm them. But don't let that absolutely bad description fool you, the game is pretty intense. The demo comes with a few missions and some compelling story to give you a good taste of what the game has in store. I enjoyed the intro missions and they really teach you how to play the game and then kick you into the action.
My only gripe about the game was really a demo limitation in that I couldn't save any progress. I didn't quite finish the demo in an hour or so but it doesn't allow you to save. That means when you come back to it you have to start at the beginning. I imagine this isn't a problem in the full meal deal.
One interesting feature I noticed as I was reading about the game on Wikipedia is the game comes with an interesting multiplayer mode. You start with an amount of points and can allocate them on certain things as you wish and go head to head with another player. Reminds me of dueling when I think about how that would play out.
In between your missions you have a base you can use to upgrade your units and do other stuff. The part of the demo I played didn't go too deep into that but it was cool to be able to see your upgraded units in your base. Oh right, XCOM brings an interesting feature to the table in that if you have units that survive missions they gain XP and get better. So you can have a badass vetran soldier you use in every battle. Just have to be careful because if they die it is permanent.
That all said install and play the demo as its available on Steam and the consoles(I played it on Steam) and let me know what you thought of it. In a world of mostly shooter games, its nice to get a tactical turn based game with some honest to God fun strategy elements to it.